Firmino is out of contract at the end of next season, as are fellow attackers Mohamed Salah and Sadio Mane.
Salah said at a media conference on Thursday that he will still be at Liverpool next season, though stopped short of committing his long-term future to the club, while Mane said he will reveal his plans after Sunday's (AEST) Champions League final against Real Madrid.
However, speaking to TNT Sports Brasil, Firmino was less cryptic, making clear his desire to stay on Merseyside.
"I am very happy here," he said. "I am grateful to God that I am here playing for a great club with great players, winning trophies, and I want to stay here. I want to be here.
"I'm happy here, so that's all that I can say."
Firmino has struggled for game time at Liverpool this season, partly due to injury and partly due to the January signing of Luis Diaz, whose arrival has seen Mane deployed in Firmino's usual role through the middle.
There was also the early season form of Diogo Jota, but the Brazil international has still made 34 appearances (17 starts) in all competitions, scoring 11 goals.